Chronic kidney disease affects about 10% of adults in the United States and 7-12% of the population worldwide. It may lead to irreversible loss of kidney function, known as end-stage renal disease (ESRD). For patients with ESRD, kidney transplantation is the preferred treatment compared to dialysis in terms of patient survival, quality of life and cost. Despite the advantages of kidney transplants, most patients with ESRD are treated with dialysis primarily because there exist an insufficient number of compatible donors for patients. The human leukocyte antigens (HLAs) of the organ donor and recipient are known to be a significant contributing factor to transplanted organ survival times due to immunogenicity, the immune response of the recipient to the transplanted organ. Mismatches between donor and recipient HLAs are associated with shorter survival times; however, it is extremely rare to identify donors that have a perfect match with recipients, so most transplants involve mismatched HLAs. Our main objective is to accurately predict survival times for kidney transplants by incorporating both data- driven models of HLA compatibility based on outcomes of past transplants and biologically-driven models of HLA immunogenicity. Accurate prediction of survival times can improve patient transplant outcomes by enabling more efficient allocation of donors and recipients, particularly by reducing the number of repeat transplants due to graft failure with a poorly matched donor. We propose to estimate HLA compatibilities using high-dimensional variable selection techniques applied to outcomes of past transplants and through a novel donor-recipient latent space model for the HLA compatibility network. We then propose to incorporate these predicted compatibilities along with biologically-driven models of HLA immunogenicity using amino acid sequences and epitopes into a multi-task classification-based survival prediction algorithm. Our proposed approach for learning integrated data- and biologically-driven models of transplant survival generalizes broadly to organ transplantation (liver, heart, pancreas, lungs) and possibly to bone marrow transplantation.